Prepare canning jars and a pressure canner before beginning.
Tuna is easier to cut evenly if partially frozen. Place the tuna fillets in the freezer for 30 to 60 minutes to partially freeze, then skin and cut into chunks.
Fill each jar with filleted tuna (no skin), leaving a 1-inch headspace. Add 1 teaspoon of salt to each pint jar or 1/2 tsp to each half pint (optional).
Wipe the rims, put on the lids, and screw on the bands to fingertip tight.
Place the jars in a pre-heated pressure canner with the water warmed to about 140 degrees F. Hot, but not yet simmering.
Process the jars at pressure for 100 minutes for both pints and half pints. Pressure depends on altitude, see table below in notes.
Allow the canner to depressurize naturally, then remove the lid carefully.
Lift out the jars and let them cool completely. Check seals and store in a cool, dark place.